A determinant formula associated with the elliptic hypergeometric integrals of type BCnBC_n

We establish a determinant formula for the bilinear form associated with the elliptic hypergeometric integrals of type $BC_n$ by studying the structure of $q$-difference equations to be satisfied by them. The determinant formula is proved by combining the $q$-difference equations of the determinant and its asymptotic analysis along the singularities. The elliptic interpolation functions of type $BC_n$ are essentially used in the study of the $q$-difference equations.Comment: 44 pages. V3: minor correction

Matrix inequalities including Furuta inequality via Riemannian mean of n-matrices

Very recently, Yamazaki has obtained an excellent generalization of Ando-Hiai inequality and a characterization of chaotic order (so called Furuta inequality for chaotic order) via weighted Riemannian mean, a kind of geometric mean, of n positive definite matrices. In this paper, by discussing extensions of Yamazaki's results, we shall obtain a generalization of Furuta inequality via weighted Riemannian mean of n-matrices

Estimations of power difference mean by Heron mean (The research of geometric structures in quantum information based on Operator Theory and related topics)

In this report, we discuss estimations of power difference mean by Heron mean. We obtain the greatest value $alpha$=$alpha$(q) and the least value $beta$=$beta$(q) such that the double inequality K_{$alpha$}(a, b)0 and q in mathbb{R}, where J_{q}(a, b)=overline{q}^{mathrm{L}{frac{a^{q+1}-b^{q+1}{a^{mathrm{q}-bmathrm{q}+1 is the power difference mean and K_{q}(a, b)=(1-q)displaystyle sqrt{ab}+qfrac{a+b}{2} is the Heron mean. We also get similar inequalities for bounded linear operators on a Hilbert space

RELATION BETWEEN RELEASE PARAMETERS AND THROWING DISTANCE OF THE JAVELIN THROW

The present study was clarified a three-dimensional examination of the relation between the release parameters and throwing distances, in order to understand the initial flight characteristics of javelins. The subjects were 57 right-handed javelin throwers. The measured throwing distances ranged from 45.25 m to 87.17 m. The elite throwers had tendency to significant positive correlation between theoretical distance and initial velocity of javelin release. Throwers who achieved throwing distances of over 70m were observed to have throwing distances that were shorter than their theoretical distances, while those whose throwing distances were under 70 m group had throwing distances that were longer than their theoretical distances. When the data were applied to initial velocity of javelin release, it was equivalent to 26 m/s